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          <a href="./Math::BigInt::Lib.html">Math::BigInt::Lib</a>
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            (<a href="./Math::BigInt::Lib.txt">source</a>,
            <a href="https://metacpan.org/pod/Math::BigInt::Lib">CPAN</a>)
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            <div id="moduleversion">version 1.999818</div>
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        <h1><a id="toc">CONTENTS</a></h1>
                  <ul>
              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#NAME">NAME</a>
              </li>
              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#SYNOPSIS">SYNOPSIS</a>
              </li>
              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#DESCRIPTION">DESCRIPTION</a>
                            <ul>
              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#General-Notes">General Notes</a>
                            <ul>
              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#API-version">API version</a>
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              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Constructors">Constructors</a>
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              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Mathematical-functions">Mathematical functions</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Bitwise-operators">Bitwise operators</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Boolean-operators">Boolean operators</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#String-conversion">String conversion</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Numeric-conversion">Numeric conversion</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Miscellaneous">Miscellaneous</a>
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          </ul>

              </li>
              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#API-version-2">API version 2</a>
                            <ul>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Constructors1">Constructors</a>
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              <li>
                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Mathematical-functions1">Mathematical functions</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#Miscellaneous1">Miscellaneous</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#WRAP-YOUR-OWN">WRAP YOUR OWN</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#BUGS">BUGS</a>
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                <a class="text-decoration-none" href="./Math::BigInt::Lib.html#LICENSE">LICENSE</a>
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          </ul>

      <h1 id="NAME"><a class="permalink" href="./Math::BigInt::Lib.html#NAME">#</a>NAME</h1>

<p>Math::BigInt::Lib - virtual parent class for Math::BigInt libraries</p>

<h1 id="SYNOPSIS"><a class="permalink" href="./Math::BigInt::Lib.html#SYNOPSIS">#</a>SYNOPSIS</h1>

<pre><code># In the backend library for Math::BigInt et al.

package Math::BigInt::MyBackend;

use Math::BigInt::lib;
our @ISA = qw&lt; Math::BigInt::lib &gt;;

sub _new { ... }
sub _str { ... }
sub _add { ... }
str _sub { ... }
...

# In your main program.

use Math::BigInt lib =&gt; &#39;MyBackend&#39;;</code></pre>

<h1 id="DESCRIPTION"><a class="permalink" href="./Math::BigInt::Lib.html#DESCRIPTION">#</a>DESCRIPTION</h1>

<p>This module provides support for big integer calculations. It is not intended to be used directly, but rather as a parent class for backend libraries used by Math::BigInt, Math::BigFloat, Math::BigRat, and related modules.</p>

<p>Other backend libraries include Math::BigInt::Calc, Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari.</p>

<p>In order to allow for multiple big integer libraries, Math::BigInt was rewritten to use a plug-in library for core math routines. Any module which conforms to the API can be used by Math::BigInt by using this in your program:</p>

<pre><code>use Math::BigInt lib =&gt; &#39;libname&#39;;</code></pre>

<p>&#39;libname&#39; is either the long name, like &#39;Math::BigInt::Pari&#39;, or only the short version, like &#39;Pari&#39;.</p>

<h2 id="General-Notes"><a class="permalink" href="./Math::BigInt::Lib.html#General-Notes">#</a><a id="General"></a>General Notes</h2>

<p>A library only needs to deal with unsigned big integers. Testing of input parameter validity is done by the caller, so there is no need to worry about underflow (e.g., in <code>_sub()</code> and <code>_dec()</code>) or about division by zero (e.g., in <code>_div()</code> and <code>_mod()</code>)) or similar cases.</p>

<p>Some libraries use methods that don&#39;t modify their argument, and some libraries don&#39;t even use objects, but rather unblessed references. Because of this, liberary methods are always called as class methods, not instance methods:</p>

<pre><code>$x = Class -&gt; method($x, $y);     # like this
$x = $x -&gt; method($y);            # not like this ...
$x -&gt; method($y);                 # ... or like this</code></pre>

<p>And with boolean methods</p>

<pre><code>$bool = Class -&gt; method($x, $y);  # like this
$bool = $x -&gt; method($y);         # not like this</code></pre>

<p>Return values are always objects, strings, Perl scalars, or true/false for comparison routines.</p>

<h3 id="API-version"><a class="permalink" href="./Math::BigInt::Lib.html#API-version">#</a><a id="API"></a>API version</h3>

<dl>

<dt id="CLASS-&gt;api_version()"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3Eapi_version()">#</a><a id="CLASS"></a><a id="CLASS-api_version"></a>CLASS-&gt;api_version()</dt>
<dd>

<p>This method is no longer used and can be omitted. Methods that are not implemented by a subclass will be inherited from this class.</p>

</dd>
</dl>

<h3 id="Constructors"><a class="permalink" href="./Math::BigInt::Lib.html#Constructors">#</a>Constructors</h3>

<p>The following methods are mandatory: _new(), _str(), _add(), and _sub(). However, computations will be very slow without _mul() and _div().</p>

<dl>

<dt id="CLASS-&gt;_new(STR)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_new(STR)">#</a><a id="CLASS1"></a><a id="CLASS-_new-STR"></a>CLASS-&gt;_new(STR)</dt>
<dd>

<p>Convert a string representing an unsigned decimal number to an object representing the same number. The input is normalized, i.e., it matches <code>^(0|[1-9]\d*)$</code>.</p>

</dd>
<dt id="CLASS-&gt;_zero()"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_zero()">#</a><a id="CLASS2"></a><a id="CLASS-_zero"></a>CLASS-&gt;_zero()</dt>
<dd>

<p>Return an object representing the number zero.</p>

</dd>
<dt id="CLASS-&gt;_one()"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_one()">#</a><a id="CLASS3"></a><a id="CLASS-_one"></a>CLASS-&gt;_one()</dt>
<dd>

<p>Return an object representing the number one.</p>

</dd>
<dt id="CLASS-&gt;_two()"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_two()">#</a><a id="CLASS4"></a><a id="CLASS-_two"></a>CLASS-&gt;_two()</dt>
<dd>

<p>Return an object representing the number two.</p>

</dd>
<dt id="CLASS-&gt;_ten()"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_ten()">#</a><a id="CLASS5"></a><a id="CLASS-_ten"></a>CLASS-&gt;_ten()</dt>
<dd>

<p>Return an object representing the number ten.</p>

</dd>
<dt id="CLASS-&gt;_from_bin(STR)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_from_bin(STR)">#</a><a id="CLASS6"></a><a id="CLASS-_from_bin-STR"></a>CLASS-&gt;_from_bin(STR)</dt>
<dd>

<p>Return an object given a string representing a binary number. The input has a &#39;0b&#39; prefix and matches the regular expression <code>^0[bB](0|1[01]*)$</code>.</p>

</dd>
<dt id="CLASS-&gt;_from_oct(STR)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_from_oct(STR)">#</a><a id="CLASS7"></a><a id="CLASS-_from_oct-STR"></a>CLASS-&gt;_from_oct(STR)</dt>
<dd>

<p>Return an object given a string representing an octal number. The input has a &#39;0&#39; prefix and matches the regular expression <code>^0[1-7]*$</code>.</p>

</dd>
<dt id="CLASS-&gt;_from_hex(STR)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_from_hex(STR)">#</a><a id="CLASS8"></a><a id="CLASS-_from_hex-STR"></a>CLASS-&gt;_from_hex(STR)</dt>
<dd>

<p>Return an object given a string representing a hexadecimal number. The input has a &#39;0x&#39; prefix and matches the regular expression <code>^0x(0|[1-9a-fA-F][\da-fA-F]*)$</code>.</p>

</dd>
<dt id="CLASS-&gt;_from_bytes(STR)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_from_bytes(STR)">#</a><a id="CLASS9"></a><a id="CLASS-_from_bytes-STR"></a>CLASS-&gt;_from_bytes(STR)</dt>
<dd>

<p>Returns an object given a byte string representing the number. The byte string is in big endian byte order, so the two-byte input string &quot;\x01\x00&quot; should give an output value representing the number 256.</p>

</dd>
<dt id="CLASS-&gt;_from_base(STR,-BASE,-COLLSEQ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_from_base(STR,-BASE,-COLLSEQ)">#</a><a id="CLASS10"></a><a id="CLASS-_from_base-STR-BASE-COLLSEQ"></a>CLASS-&gt;_from_base(STR, BASE, COLLSEQ)</dt>
<dd>

<p>Returns an object given a string STR, a base BASE, and a collation sequence COLLSEQ. Each character in STR represents a numerical value identical to the character&#39;s position in COLLSEQ. All characters in STR must be present in COLLSEQ.</p>

<p>If BASE is less than or equal to 94, and a collation sequence is not specified, the following default collation sequence is used. It contains of all the 94 printable ASCII characters except space/blank:</p>

<pre><code class="plaintext">0123456789                  # ASCII  48 to  57
ABCDEFGHIJKLMNOPQRSTUVWXYZ  # ASCII  65 to  90
abcdefghijklmnopqrstuvwxyz  # ASCII  97 to 122
!&quot;#$%&amp;&#39;()*+,-./             # ASCII  33 to  47
:;&lt;=&gt;?@                     # ASCII  58 to  64
[\]^_`                      # ASCII  91 to  96
{|}~                        # ASCII 123 to 126</code></pre>

<p>If the default collation sequence is used, and the BASE is less than or equal to 36, the letter case in STR is ignored.</p>

<p>For instance, with base 3 and collation sequence &quot;-/|&quot;, the character &quot;-&quot; represents 0, &quot;/&quot; represents 1, and &quot;|&quot; represents 2. So if STR is &quot;/|-&quot;, the output is 1 * 3**2 + 2 * 3**1 + 0 * 3**0 = 15.</p>

<p>The following examples show standard binary, octal, decimal, and hexadecimal conversion. All examples return 250.</p>

<pre><code>$x = $class -&gt; _from_base(&quot;11111010&quot;, 2)
$x = $class -&gt; _from_base(&quot;372&quot;, 8)
$x = $class -&gt; _from_base(&quot;250&quot;, 10)
$x = $class -&gt; _from_base(&quot;FA&quot;, 16)</code></pre>

<p>Some more examples, all returning 250:</p>

<pre><code>$x = $class -&gt; _from_base(&quot;100021&quot;, 3)
$x = $class -&gt; _from_base(&quot;3322&quot;, 4)
$x = $class -&gt; _from_base(&quot;2000&quot;, 5)
$x = $class -&gt; _from_base(&quot;caaa&quot;, 5, &quot;abcde&quot;)
$x = $class -&gt; _from_base(&quot;42&quot;, 62)
$x = $class -&gt; _from_base(&quot;2!&quot;, 94)</code></pre>

</dd>
</dl>

<h3 id="Mathematical-functions"><a class="permalink" href="./Math::BigInt::Lib.html#Mathematical-functions">#</a><a id="Mathematical"></a>Mathematical functions</h3>

<dl>

<dt id="CLASS-&gt;_add(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_add(OBJ1,-OBJ2)">#</a><a id="CLASS11"></a><a id="CLASS-_add-OBJ1-OBJ2"></a>CLASS-&gt;_add(OBJ1, OBJ2)</dt>
<dd>

<p>Returns the result of adding OBJ2 to OBJ1.</p>

</dd>
<dt id="CLASS-&gt;_mul(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_mul(OBJ1,-OBJ2)">#</a><a id="CLASS12"></a><a id="CLASS-_mul-OBJ1-OBJ2"></a>CLASS-&gt;_mul(OBJ1, OBJ2)</dt>
<dd>

<p>Returns the result of multiplying OBJ2 and OBJ1.</p>

</dd>
<dt id="CLASS-&gt;_div(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_div(OBJ1,-OBJ2)">#</a><a id="CLASS13"></a><a id="CLASS-_div-OBJ1-OBJ2"></a>CLASS-&gt;_div(OBJ1, OBJ2)</dt>
<dd>

<p>In scalar context, returns the quotient after dividing OBJ1 by OBJ2 and truncating the result to an integer. In list context, return the quotient and the remainder.</p>

</dd>
<dt id="CLASS-&gt;_sub(OBJ1,-OBJ2,-FLAG)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_sub(OBJ1,-OBJ2,-FLAG)">#</a><a id="CLASS14"></a><a id="CLASS-_sub-OBJ1-OBJ2-FLAG"></a>CLASS-&gt;_sub(OBJ1, OBJ2, FLAG)</dt>
<dd>

</dd>
<dt id="CLASS-&gt;_sub(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_sub(OBJ1,-OBJ2)">#</a><a id="CLASS15"></a><a id="CLASS-_sub-OBJ1-OBJ2"></a>CLASS-&gt;_sub(OBJ1, OBJ2)</dt>
<dd>

<p>Returns the result of subtracting OBJ2 by OBJ1. If <code>flag</code> is false or omitted, OBJ1 might be modified. If <code>flag</code> is true, OBJ2 might be modified.</p>

</dd>
<dt id="CLASS-&gt;_dec(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_dec(OBJ)">#</a><a id="CLASS16"></a><a id="CLASS-_dec-OBJ"></a>CLASS-&gt;_dec(OBJ)</dt>
<dd>

<p>Returns the result after decrementing OBJ by one.</p>

</dd>
<dt id="CLASS-&gt;_inc(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_inc(OBJ)">#</a><a id="CLASS17"></a><a id="CLASS-_inc-OBJ"></a>CLASS-&gt;_inc(OBJ)</dt>
<dd>

<p>Returns the result after incrementing OBJ by one.</p>

</dd>
<dt id="CLASS-&gt;_mod(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_mod(OBJ1,-OBJ2)">#</a><a id="CLASS18"></a><a id="CLASS-_mod-OBJ1-OBJ2"></a>CLASS-&gt;_mod(OBJ1, OBJ2)</dt>
<dd>

<p>Returns OBJ1 modulo OBJ2, i.e., the remainder after dividing OBJ1 by OBJ2.</p>

</dd>
<dt id="CLASS-&gt;_sqrt(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_sqrt(OBJ)">#</a><a id="CLASS19"></a><a id="CLASS-_sqrt-OBJ"></a>CLASS-&gt;_sqrt(OBJ)</dt>
<dd>

<p>Returns the square root of OBJ, truncated to an integer.</p>

</dd>
<dt id="CLASS-&gt;_root(OBJ,-N)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_root(OBJ,-N)">#</a><a id="CLASS20"></a><a id="CLASS-_root-OBJ-N"></a>CLASS-&gt;_root(OBJ, N)</dt>
<dd>

<p>Returns the Nth root of OBJ, truncated to an integer.</p>

</dd>
<dt id="CLASS-&gt;_fac(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_fac(OBJ)">#</a><a id="CLASS21"></a><a id="CLASS-_fac-OBJ"></a>CLASS-&gt;_fac(OBJ)</dt>
<dd>

<p>Returns the factorial of OBJ, i.e., the product of all positive integers up to and including OBJ.</p>

</dd>
<dt id="CLASS-&gt;_dfac(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_dfac(OBJ)">#</a><a id="CLASS22"></a><a id="CLASS-_dfac-OBJ"></a>CLASS-&gt;_dfac(OBJ)</dt>
<dd>

<p>Returns the double factorial of OBJ. If OBJ is an even integer, returns the product of all positive, even integers up to and including OBJ, i.e., 2*4*6*...*OBJ. If OBJ is an odd integer, returns the product of all positive, odd integers, i.e., 1*3*5*...*OBJ.</p>

</dd>
<dt id="CLASS-&gt;_pow(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_pow(OBJ1,-OBJ2)">#</a><a id="CLASS23"></a><a id="CLASS-_pow-OBJ1-OBJ2"></a>CLASS-&gt;_pow(OBJ1, OBJ2)</dt>
<dd>

<p>Returns OBJ1 raised to the power of OBJ2. By convention, 0**0 = 1.</p>

</dd>
<dt id="CLASS-&gt;_modinv(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_modinv(OBJ1,-OBJ2)">#</a><a id="CLASS24"></a><a id="CLASS-_modinv-OBJ1-OBJ2"></a>CLASS-&gt;_modinv(OBJ1, OBJ2)</dt>
<dd>

<p>Returns the modular multiplicative inverse, i.e., return OBJ3 so that</p>

<pre><code class="plaintext">(OBJ3 * OBJ1) % OBJ2 = 1 % OBJ2</code></pre>

<p>The result is returned as two arguments. If the modular multiplicative inverse does not exist, both arguments are undefined. Otherwise, the arguments are a number (object) and its sign (&quot;+&quot; or &quot;-&quot;).</p>

<p>The output value, with its sign, must either be a positive value in the range 1,2,...,OBJ2-1 or the same value subtracted OBJ2. For instance, if the input arguments are objects representing the numbers 7 and 5, the method must either return an object representing the number 3 and a &quot;+&quot; sign, since (3*7) % 5 = 1 % 5, or an object representing the number 2 and a &quot;-&quot; sign, since (-2*7) % 5 = 1 % 5.</p>

</dd>
<dt id="CLASS-&gt;_modpow(OBJ1,-OBJ2,-OBJ3)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_modpow(OBJ1,-OBJ2,-OBJ3)">#</a><a id="CLASS25"></a><a id="CLASS-_modpow-OBJ1-OBJ2-OBJ3"></a>CLASS-&gt;_modpow(OBJ1, OBJ2, OBJ3)</dt>
<dd>

<p>Returns the modular exponentiation, i.e., (OBJ1 ** OBJ2) % OBJ3.</p>

</dd>
<dt id="CLASS-&gt;_rsft(OBJ,-N,-B)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_rsft(OBJ,-N,-B)">#</a><a id="CLASS26"></a><a id="CLASS-_rsft-OBJ-N-B"></a>CLASS-&gt;_rsft(OBJ, N, B)</dt>
<dd>

<p>Returns the result after shifting OBJ N digits to thee right in base B. This is equivalent to performing integer division by B**N and discarding the remainder, except that it might be much faster.</p>

<p>For instance, if the object $obj represents the hexadecimal number 0xabcde, then <code>_rsft($obj, 2, 16)</code> returns an object representing the number 0xabc. The &quot;remainer&quot;, 0xde, is discarded and not returned.</p>

</dd>
<dt id="CLASS-&gt;_lsft(OBJ,-N,-B)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_lsft(OBJ,-N,-B)">#</a><a id="CLASS27"></a><a id="CLASS-_lsft-OBJ-N-B"></a>CLASS-&gt;_lsft(OBJ, N, B)</dt>
<dd>

<p>Returns the result after shifting OBJ N digits to the left in base B. This is equivalent to multiplying by B**N, except that it might be much faster.</p>

</dd>
<dt id="CLASS-&gt;_log_int(OBJ,-B)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_log_int(OBJ,-B)">#</a><a id="CLASS28"></a><a id="CLASS-_log_int-OBJ-B"></a>CLASS-&gt;_log_int(OBJ, B)</dt>
<dd>

<p>Returns the logarithm of OBJ to base BASE truncted to an integer. This method has two output arguments, the OBJECT and a STATUS. The STATUS is Perl scalar; it is 1 if OBJ is the exact result, 0 if the result was truncted to give OBJ, and undef if it is unknown whether OBJ is the exact result.</p>

</dd>
<dt id="CLASS-&gt;_gcd(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_gcd(OBJ1,-OBJ2)">#</a><a id="CLASS29"></a><a id="CLASS-_gcd-OBJ1-OBJ2"></a>CLASS-&gt;_gcd(OBJ1, OBJ2)</dt>
<dd>

<p>Returns the greatest common divisor of OBJ1 and OBJ2.</p>

</dd>
<dt id="CLASS-&gt;_lcm(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_lcm(OBJ1,-OBJ2)">#</a><a id="CLASS30"></a><a id="CLASS-_lcm-OBJ1-OBJ2"></a>CLASS-&gt;_lcm(OBJ1, OBJ2)</dt>
<dd>

<p>Return the least common multiple of OBJ1 and OBJ2.</p>

</dd>
<dt id="CLASS-&gt;_fib(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_fib(OBJ)">#</a><a id="CLASS31"></a><a id="CLASS-_fib-OBJ"></a>CLASS-&gt;_fib(OBJ)</dt>
<dd>

<p>In scalar context, returns the nth Fibonacci number: _fib(0) returns 0, _fib(1) returns 1, _fib(2) returns 1, _fib(3) returns 2 etc. In list context, returns the Fibonacci numbers from F(0) to F(n): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...</p>

</dd>
<dt id="CLASS-&gt;_lucas(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_lucas(OBJ)">#</a><a id="CLASS32"></a><a id="CLASS-_lucas-OBJ"></a>CLASS-&gt;_lucas(OBJ)</dt>
<dd>

<p>In scalar context, returns the nth Lucas number: _lucas(0) returns 2, _lucas(1) returns 1, _lucas(2) returns 3, etc. In list context, returns the Lucas numbers from L(0) to L(n): 2, 1, 3, 4, 7, 11, 18, 29,47, 76, ...</p>

</dd>
</dl>

<h3 id="Bitwise-operators"><a class="permalink" href="./Math::BigInt::Lib.html#Bitwise-operators">#</a><a id="Bitwise"></a>Bitwise operators</h3>

<dl>

<dt id="CLASS-&gt;_and(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_and(OBJ1,-OBJ2)">#</a><a id="CLASS33"></a><a id="CLASS-_and-OBJ1-OBJ2"></a>CLASS-&gt;_and(OBJ1, OBJ2)</dt>
<dd>

<p>Returns bitwise and.</p>

</dd>
<dt id="CLASS-&gt;_or(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_or(OBJ1,-OBJ2)">#</a><a id="CLASS34"></a><a id="CLASS-_or-OBJ1-OBJ2"></a>CLASS-&gt;_or(OBJ1, OBJ2)</dt>
<dd>

<p>Returns bitwise or.</p>

</dd>
<dt id="CLASS-&gt;_xor(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_xor(OBJ1,-OBJ2)">#</a><a id="CLASS35"></a><a id="CLASS-_xor-OBJ1-OBJ2"></a>CLASS-&gt;_xor(OBJ1, OBJ2)</dt>
<dd>

<p>Returns bitwise exclusive or.</p>

</dd>
<dt id="CLASS-&gt;_sand(OBJ1,-OBJ2,-SIGN1,-SIGN2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_sand(OBJ1,-OBJ2,-SIGN1,-SIGN2)">#</a><a id="CLASS36"></a><a id="CLASS-_sand-OBJ1-OBJ2-SIGN1-SIGN2"></a>CLASS-&gt;_sand(OBJ1, OBJ2, SIGN1, SIGN2)</dt>
<dd>

<p>Returns bitwise signed and.</p>

</dd>
<dt id="CLASS-&gt;_sor(OBJ1,-OBJ2,-SIGN1,-SIGN2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_sor(OBJ1,-OBJ2,-SIGN1,-SIGN2)">#</a><a id="CLASS37"></a><a id="CLASS-_sor-OBJ1-OBJ2-SIGN1-SIGN2"></a>CLASS-&gt;_sor(OBJ1, OBJ2, SIGN1, SIGN2)</dt>
<dd>

<p>Returns bitwise signed or.</p>

</dd>
<dt id="CLASS-&gt;_sxor(OBJ1,-OBJ2,-SIGN1,-SIGN2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_sxor(OBJ1,-OBJ2,-SIGN1,-SIGN2)">#</a><a id="CLASS38"></a><a id="CLASS-_sxor-OBJ1-OBJ2-SIGN1-SIGN2"></a>CLASS-&gt;_sxor(OBJ1, OBJ2, SIGN1, SIGN2)</dt>
<dd>

<p>Returns bitwise signed exclusive or.</p>

</dd>
</dl>

<h3 id="Boolean-operators"><a class="permalink" href="./Math::BigInt::Lib.html#Boolean-operators">#</a><a id="Boolean"></a>Boolean operators</h3>

<dl>

<dt id="CLASS-&gt;_is_zero(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_is_zero(OBJ)">#</a><a id="CLASS39"></a><a id="CLASS-_is_zero-OBJ"></a>CLASS-&gt;_is_zero(OBJ)</dt>
<dd>

<p>Returns a true value if OBJ is zero, and false value otherwise.</p>

</dd>
<dt id="CLASS-&gt;_is_one(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_is_one(OBJ)">#</a><a id="CLASS40"></a><a id="CLASS-_is_one-OBJ"></a>CLASS-&gt;_is_one(OBJ)</dt>
<dd>

<p>Returns a true value if OBJ is one, and false value otherwise.</p>

</dd>
<dt id="CLASS-&gt;_is_two(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_is_two(OBJ)">#</a><a id="CLASS41"></a><a id="CLASS-_is_two-OBJ"></a>CLASS-&gt;_is_two(OBJ)</dt>
<dd>

<p>Returns a true value if OBJ is two, and false value otherwise.</p>

</dd>
<dt id="CLASS-&gt;_is_ten(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_is_ten(OBJ)">#</a><a id="CLASS42"></a><a id="CLASS-_is_ten-OBJ"></a>CLASS-&gt;_is_ten(OBJ)</dt>
<dd>

<p>Returns a true value if OBJ is ten, and false value otherwise.</p>

</dd>
<dt id="CLASS-&gt;_is_even(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_is_even(OBJ)">#</a><a id="CLASS43"></a><a id="CLASS-_is_even-OBJ"></a>CLASS-&gt;_is_even(OBJ)</dt>
<dd>

<p>Return a true value if OBJ is an even integer, and a false value otherwise.</p>

</dd>
<dt id="CLASS-&gt;_is_odd(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_is_odd(OBJ)">#</a><a id="CLASS44"></a><a id="CLASS-_is_odd-OBJ"></a>CLASS-&gt;_is_odd(OBJ)</dt>
<dd>

<p>Return a true value if OBJ is an even integer, and a false value otherwise.</p>

</dd>
<dt id="CLASS-&gt;_acmp(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_acmp(OBJ1,-OBJ2)">#</a><a id="CLASS45"></a><a id="CLASS-_acmp-OBJ1-OBJ2"></a>CLASS-&gt;_acmp(OBJ1, OBJ2)</dt>
<dd>

<p>Compare OBJ1 and OBJ2 and return -1, 0, or 1, if OBJ1 is numerically less than, equal to, or larger than OBJ2, respectively.</p>

</dd>
</dl>

<h3 id="String-conversion"><a class="permalink" href="./Math::BigInt::Lib.html#String-conversion">#</a><a id="String"></a>String conversion</h3>

<dl>

<dt id="CLASS-&gt;_str(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_str(OBJ)">#</a><a id="CLASS46"></a><a id="CLASS-_str-OBJ"></a>CLASS-&gt;_str(OBJ)</dt>
<dd>

<p>Returns a string representing OBJ in decimal notation. The returned string should have no leading zeros, i.e., it should match <code>^(0|[1-9]\d*)$</code>.</p>

</dd>
<dt id="CLASS-&gt;_to_bin(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_to_bin(OBJ)">#</a><a id="CLASS47"></a><a id="CLASS-_to_bin-OBJ"></a>CLASS-&gt;_to_bin(OBJ)</dt>
<dd>

<p>Returns the binary string representation of OBJ.</p>

</dd>
<dt id="CLASS-&gt;_to_oct(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_to_oct(OBJ)">#</a><a id="CLASS48"></a><a id="CLASS-_to_oct-OBJ"></a>CLASS-&gt;_to_oct(OBJ)</dt>
<dd>

<p>Returns the octal string representation of the number.</p>

</dd>
<dt id="CLASS-&gt;_to_hex(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_to_hex(OBJ)">#</a><a id="CLASS49"></a><a id="CLASS-_to_hex-OBJ"></a>CLASS-&gt;_to_hex(OBJ)</dt>
<dd>

<p>Returns the hexadecimal string representation of the number.</p>

</dd>
<dt id="CLASS-&gt;_to_bytes(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_to_bytes(OBJ)">#</a><a id="CLASS50"></a><a id="CLASS-_to_bytes-OBJ"></a>CLASS-&gt;_to_bytes(OBJ)</dt>
<dd>

<p>Returns a byte string representation of OBJ. The byte string is in big endian byte order, so if OBJ represents the number 256, the output should be the two-byte string &quot;\x01\x00&quot;.</p>

</dd>
<dt id="CLASS-&gt;_to_base(OBJ,-BASE,-COLLSEQ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_to_base(OBJ,-BASE,-COLLSEQ)">#</a><a id="CLASS51"></a><a id="CLASS-_to_base-OBJ-BASE-COLLSEQ"></a>CLASS-&gt;_to_base(OBJ, BASE, COLLSEQ)</dt>
<dd>

<p>Returns a string representation of OBJ in base BASE with collation sequence COLLSEQ.</p>

<pre><code>$val = $class -&gt; _new(&quot;210&quot;);
$str = $class -&gt; _to_base($val, 10, &quot;xyz&quot;)  # $str is &quot;zyx&quot;

$val = $class -&gt; _new(&quot;32&quot;);
$str = $class -&gt; _to_base($val, 2, &quot;-|&quot;)  # $str is &quot;|-----&quot;</code></pre>

<p>See _from_base() for more information.</p>

</dd>
<dt id="CLASS-&gt;_as_bin(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_as_bin(OBJ)">#</a><a id="CLASS52"></a><a id="CLASS-_as_bin-OBJ"></a>CLASS-&gt;_as_bin(OBJ)</dt>
<dd>

<p>Like <code>_to_bin()</code> but with a &#39;0b&#39; prefix.</p>

</dd>
<dt id="CLASS-&gt;_as_oct(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_as_oct(OBJ)">#</a><a id="CLASS53"></a><a id="CLASS-_as_oct-OBJ"></a>CLASS-&gt;_as_oct(OBJ)</dt>
<dd>

<p>Like <code>_to_oct()</code> but with a &#39;0&#39; prefix.</p>

</dd>
<dt id="CLASS-&gt;_as_hex(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_as_hex(OBJ)">#</a><a id="CLASS54"></a><a id="CLASS-_as_hex-OBJ"></a>CLASS-&gt;_as_hex(OBJ)</dt>
<dd>

<p>Like <code>_to_hex()</code> but with a &#39;0x&#39; prefix.</p>

</dd>
<dt id="CLASS-&gt;_as_bytes(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_as_bytes(OBJ)">#</a><a id="CLASS55"></a><a id="CLASS-_as_bytes-OBJ"></a>CLASS-&gt;_as_bytes(OBJ)</dt>
<dd>

<p>This is an alias to <code>_to_bytes()</code>.</p>

</dd>
</dl>

<h3 id="Numeric-conversion"><a class="permalink" href="./Math::BigInt::Lib.html#Numeric-conversion">#</a><a id="Numeric"></a>Numeric conversion</h3>

<dl>

<dt id="CLASS-&gt;_num(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_num(OBJ)">#</a><a id="CLASS56"></a><a id="CLASS-_num-OBJ"></a>CLASS-&gt;_num(OBJ)</dt>
<dd>

<p>Returns a Perl scalar number representing the number OBJ as close as possible. Since Perl scalars have limited precision, the returned value might not be exactly the same as OBJ.</p>

</dd>
</dl>

<h3 id="Miscellaneous"><a class="permalink" href="./Math::BigInt::Lib.html#Miscellaneous">#</a>Miscellaneous</h3>

<dl>

<dt id="CLASS-&gt;_copy(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_copy(OBJ)">#</a><a id="CLASS57"></a><a id="CLASS-_copy-OBJ"></a>CLASS-&gt;_copy(OBJ)</dt>
<dd>

<p>Returns a true copy OBJ.</p>

</dd>
<dt id="CLASS-&gt;_len(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_len(OBJ)">#</a><a id="CLASS58"></a><a id="CLASS-_len-OBJ"></a>CLASS-&gt;_len(OBJ)</dt>
<dd>

<p>Returns the number of the decimal digits in OBJ. The output is a Perl scalar.</p>

</dd>
<dt id="CLASS-&gt;_zeros(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_zeros(OBJ)">#</a><a id="CLASS59"></a><a id="CLASS-_zeros-OBJ"></a>CLASS-&gt;_zeros(OBJ)</dt>
<dd>

<p>Returns the number of trailing decimal zeros. The output is a Perl scalar. The number zero has no trailing decimal zeros.</p>

</dd>
<dt id="CLASS-&gt;_digit(OBJ,-N)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_digit(OBJ,-N)">#</a><a id="CLASS60"></a><a id="CLASS-_digit-OBJ-N"></a>CLASS-&gt;_digit(OBJ, N)</dt>
<dd>

<p>Returns the Nth digit in OBJ as a Perl scalar. N is a Perl scalar, where zero refers to the rightmost (least significant) digit, and negative values count from the left (most significant digit). If $obj represents the number 123, then</p>

<pre><code>CLASS-&gt;_digit($obj,  0)     # returns 3
CLASS-&gt;_digit($obj,  1)     # returns 2
CLASS-&gt;_digit($obj,  2)     # returns 1
CLASS-&gt;_digit($obj, -1)     # returns 1</code></pre>

</dd>
<dt id="CLASS-&gt;_digitsum(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_digitsum(OBJ)">#</a><a id="CLASS61"></a><a id="CLASS-_digitsum-OBJ"></a>CLASS-&gt;_digitsum(OBJ)</dt>
<dd>

<p>Returns the sum of the base 10 digits.</p>

</dd>
<dt id="CLASS-&gt;_check(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_check(OBJ)">#</a><a id="CLASS62"></a><a id="CLASS-_check-OBJ"></a>CLASS-&gt;_check(OBJ)</dt>
<dd>

<p>Returns true if the object is invalid and false otherwise. Preferably, the true value is a string describing the problem with the object. This is a check routine to test the internal state of the object for corruption.</p>

</dd>
<dt id="CLASS-&gt;_set(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_set(OBJ)">#</a><a id="CLASS63"></a><a id="CLASS-_set-OBJ"></a>CLASS-&gt;_set(OBJ)</dt>
<dd>

<p>xxx</p>

</dd>
</dl>

<h2 id="API-version-2"><a class="permalink" href="./Math::BigInt::Lib.html#API-version-2">#</a><a id="API1"></a>API version 2</h2>

<p>The following methods are required for an API version of 2 or greater.</p>

<h3 id="Constructors1"><a class="permalink" href="./Math::BigInt::Lib.html#Constructors1">#</a>Constructors</h3>

<dl>

<dt id="CLASS-&gt;_1ex(N)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_1ex(N)">#</a><a id="CLASS64"></a><a id="CLASS-_1ex-N"></a>CLASS-&gt;_1ex(N)</dt>
<dd>

<p>Return an object representing the number 10**N where N &gt;= 0 is a Perl scalar.</p>

</dd>
</dl>

<h3 id="Mathematical-functions1"><a class="permalink" href="./Math::BigInt::Lib.html#Mathematical-functions1">#</a><a id="Mathematical1"></a>Mathematical functions</h3>

<dl>

<dt id="CLASS-&gt;_nok(OBJ1,-OBJ2)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_nok(OBJ1,-OBJ2)">#</a><a id="CLASS65"></a><a id="CLASS-_nok-OBJ1-OBJ2"></a>CLASS-&gt;_nok(OBJ1, OBJ2)</dt>
<dd>

<p>Return the binomial coefficient OBJ1 over OBJ1.</p>

</dd>
</dl>

<h3 id="Miscellaneous1"><a class="permalink" href="./Math::BigInt::Lib.html#Miscellaneous1">#</a>Miscellaneous</h3>

<dl>

<dt id="CLASS-&gt;_alen(OBJ)"><a class="permalink" href="./Math::BigInt::Lib.html#CLASS-%3E_alen(OBJ)">#</a><a id="CLASS66"></a><a id="CLASS-_alen-OBJ"></a>CLASS-&gt;_alen(OBJ)</dt>
<dd>

<p>Return the approximate number of decimal digits of the object. The output is a Perl scalar.</p>

</dd>
</dl>

<h1 id="WRAP-YOUR-OWN"><a class="permalink" href="./Math::BigInt::Lib.html#WRAP-YOUR-OWN">#</a><a id="WRAP"></a>WRAP YOUR OWN</h1>

<p>If you want to port your own favourite C library for big numbers to the Math::BigInt interface, you can take any of the already existing modules as a rough guideline. You should really wrap up the latest Math::BigInt and Math::BigFloat testsuites with your module, and replace in them any of the following:</p>

<pre><code>use Math::BigInt;</code></pre>

<p>by this:</p>

<pre><code>use Math::BigInt lib =&gt; &#39;yourlib&#39;;</code></pre>

<p>This way you ensure that your library really works 100% within Math::BigInt.</p>

<h1 id="BUGS"><a class="permalink" href="./Math::BigInt::Lib.html#BUGS">#</a>BUGS</h1>

<p>Please report any bugs or feature requests to <code>bug-math-bigint at rt.cpan.org</code>, or through the web interface at <a href="https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt">https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt</a> (requires login). We will be notified, and then you&#39;ll automatically be notified of progress on your bug as I make changes.</p>

<h1 id="SUPPORT"><a class="permalink" href="./Math::BigInt::Lib.html#SUPPORT">#</a>SUPPORT</h1>

<p>You can find documentation for this module with the perldoc command.</p>

<pre><code class="plaintext">perldoc Math::BigInt::Calc</code></pre>

<p>You can also look for information at:</p>

<ul>

<li><p>RT: CPAN&#39;s request tracker</p>

<p><a href="https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt">https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt</a></p>

</li>
<li><p>AnnoCPAN: Annotated CPAN documentation</p>

<p><a href="http://annocpan.org/dist/Math-BigInt">http://annocpan.org/dist/Math-BigInt</a></p>

</li>
<li><p>CPAN Ratings</p>

<p><a href="https://cpanratings.perl.org/dist/Math-BigInt">https://cpanratings.perl.org/dist/Math-BigInt</a></p>

</li>
<li><p>MetaCPAN</p>

<p><a href="https://metacpan.org/release/Math-BigInt">https://metacpan.org/release/Math-BigInt</a></p>

</li>
<li><p>CPAN Testers Matrix</p>

<p><a href="http://matrix.cpantesters.org/?dist=Math-BigInt">http://matrix.cpantesters.org/?dist=Math-BigInt</a></p>

</li>
<li><p>The Bignum mailing list</p>

<ul>

<li><p>Post to mailing list</p>

<p><code>bignum at lists.scsys.co.uk</code></p>

</li>
<li><p>View mailing list</p>

<p><a href="http://lists.scsys.co.uk/pipermail/bignum/">http://lists.scsys.co.uk/pipermail/bignum/</a></p>

</li>
<li><p>Subscribe/Unsubscribe</p>

<p><a href="http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum">http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum</a></p>

</li>
</ul>

</li>
</ul>

<h1 id="LICENSE"><a class="permalink" href="./Math::BigInt::Lib.html#LICENSE">#</a>LICENSE</h1>

<p>This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.</p>

<h1 id="AUTHOR"><a class="permalink" href="./Math::BigInt::Lib.html#AUTHOR">#</a>AUTHOR</h1>

<p>Peter John Acklam, &lt;pjacklam@online.no&gt;</p>

<p>Code and documentation based on the Math::BigInt::Calc module by Tels &lt;nospam-abuse@bloodgate.com&gt;</p>

<h1 id="SEE-ALSO"><a class="permalink" href="./Math::BigInt::Lib.html#SEE-ALSO">#</a><a id="SEE"></a>SEE ALSO</h1>

<p><a href="./Math::BigInt.html">Math::BigInt</a>, <a href="./Math::BigInt::Calc.html">Math::BigInt::Calc</a>, <a href="./Math::BigInt::GMP.html">Math::BigInt::GMP</a>, <a href="./Math::BigInt::FastCalc.html">Math::BigInt::FastCalc</a> and <a href="./Math::BigInt::Pari.html">Math::BigInt::Pari</a>.</p>


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